SciPost Submission Page

Mixing times and cutoffs in open quadratic fermionic systems

by Eric Vernier

Submission summary

As Contributors: Eric Vernier
Arxiv Link: (pdf)
Date accepted: 2020-10-09
Date submitted: 2020-09-18 09:15
Submitted by: Vernier, Eric
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


In classical probability theory, the term "cutoff" describes the property of some Markov chains to jump from (close to) their initial configuration to (close to) completely mixed in a very narrow window of time. We investigate how coherent quantum evolution affects the mixing properties in two fermionic quantum models (the "gain/loss" and "topological" models), whose time evolution is governed by a Lindblad equation quadratic in fermionic operators, allowing for a straightforward exact solution. We check that the phenomenon of cutoff extends to the quantum case and examine with some care how the mixing properties depend on the initial state, drawing different regimes of our models with qualitatively different behaviour. In the topological case, we further show how the mixing properties are affected by the presence of a long-lived edge zero mode when taking open boundary conditions.

Published as SciPost Phys. 9, 049 (2020)

Author comments upon resubmission

Please find attached a new version of my manuscript, where I believe I have addressed all issues previously raised by the referees. In particular, the discussion on the phase diagram of the topological model has been improved, and the regimes of interest better specified.
Furthermore, the typesetting of Eq. (60) has been improved.

List of changes

- A figure (Fig. 3) has been added, clarifying the phase diagram of the topological model and in particular the difference between a small dissipation regime and a "quantum Zeno" regime
- In Section 4.4, the regimes of interest for the topological model have been better specified
- The typesetting of Eq. (60) has been improved
- references have been added
- few extra minor corrections

Reports on this Submission

Anonymous Report 1 on 2020-10-1 Invited Report


The author has responded to all my concerns, the paper is good to go.

  • validity: high
  • significance: high
  • originality: good
  • clarity: high
  • formatting: perfect
  • grammar: perfect

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